Linked Questions

4
votes
3answers
224 views

Designing a CFG that produces as many c's as the difference of numbers of a's and b's

The question is to design a CFG for the language of words that have as many c's as the difference of numbers of a's and b's, that is $\qquad\displaystyle L = \{(a^l)(b^m)(c^n) \mid l, m \in \mathbb{N}...
2
votes
1answer
566 views

Show that language generated by grammar is regular

We have grammar with nonterminals $ X_1,...X_n$ terminals $V_t$ and rewriting rules of form: $X_i \rightarrow a \in V_t $ $X_i \rightarrow X_jX_k, \ i \ge j , \ i > k $ How can I show that ...
2
votes
2answers
182 views

Proof for BFS and DFS equivalence

I'm trying to prove (by induction) that BFS in equivalent to DFS, in the sense that they return the same set of visited nodes, but I'm stuck in the middle of some of the cases. Let $G$ be a directed ...
0
votes
2answers
777 views

Context-free grammar for“not-at-all” palindromes

I need to bulid a context-free grammar for $\qquad \mathscr{L_4}=\{w\in\{a,b,c\}^* \mid w\text{ is not palindrome at all}\}$ Not palindrom at all: We will say that a word $w$ is not palindrome at ...
0
votes
1answer
467 views

Regular expression for a binary number that includes “10” and has an odd number of 0's

I have been struggling trying to write a regular expression for a binary number that includes "10" and has an odd number of 0's, so far I have (1) * (00) * 10(1010) * (00) * (1) * but it doesn't ...
1
vote
0answers
534 views

How to describe the language generated by S → a | S + S | S S | S * | ( S )

I am trying to solve the following problem from Aho, et al., Compilers: Principles, Techniques, & Tools (2nd ed.), exercise 2.2.2e: What language is generated by the following grammar? $S\...
5
votes
1answer
174 views

Proof by induction over rules for mutually recursive relations

Consider the (big-step) semantics of a language ($a, e$ terms, $v$ values), defined by two mutually recursive relations, $\downarrow$ and $\Downarrow$, given by a set of rule-schemata (simplified): $\...
0
votes
0answers
464 views

Describe the language generated by a given context free grammar

I had an exercise: Describe the language generated by the following given context free grammar and prove it by induction. $$\begin{align} S &\to SA \mid \epsilon \\ A &\to aS \mid bA \...
1
vote
2answers
165 views

Show that a language cannot be generated by linear grammar

I have a language $ L= \{ w \in \{a,b\}^* ; |w|_b=2i, i \ge 0 \}$ that is a language with even number of b's. I found a grammar for it with these rules: $S \rightarrow aS \ | \ bL \ | \ \lambda $...
1
vote
1answer
272 views

Determining Language from Context Free Grammar

I am trying to understand how to write the language given the predicates of the context free grammar. As an example, I have the following grammar: $S \to 0B \mid 1A$ $A \to 0 \mid 0S \mid 1AA$ $B \...
2
votes
1answer
269 views

Prove the equivalence between a CFG and a Context free language

I have to prove that the language $L=\{a^ib^j:2i=3j+1\}$ and the CFG G with the following rewrite rules: $S\rightarrow a^2Tb$ $T\rightarrow a^3Tb^2 |\epsilon$ are equivalent to each other. I'm ...
0
votes
1answer
243 views

Why is this language not context free?

I been watching tutorials about how to check if a language is not context-free and in 1 video there was a language: L = {a^n b^n c^n | n ≥ 0} and they used a pumping lemma to prove that it's not ...
1
vote
2answers
298 views

Context-free grammar for binary words

I am supposed to create CFG for this languague: $L= \{w : w \in \{a, b\}^*, |w_b| = 3k, k \geq 0 \}$ where $|w_b|$ is count of terminals $b$ in $w$. For example: aa - OK, no 'b' abb - wrong, only ...
1
vote
1answer
207 views

Prove L = L(R) based on a regular expression

I'm given the following language: L = {w∈{0,1}* | w ends in 010 and contains 011} The task is to find a regular expression R that describes this language and ...
2
votes
2answers
69 views

Interpreting a Language

I'm having trouble understanding some language notation, primarily what rules I can take away from it. The language is as follows: $\qquad L = \{a^n b^m b^p c^p b^{n-m} \mid n > 0, m < n, p >...

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